In devising a covariant scheme for updating we draw primarily from the work of IAC [1]}[2]}. To review briefly, a primary assumption in the IAC approach was the adoption of a canonical framework for governing the coupled dynamics of \(\rho _{\sigma }\)  and \(\phi _{\sigma }\) , expressed more conveniently through the transformed variable \(\Phi _{\sigma }\) . Although this is certainly a strong assumption, it is one that has some justification. On one front, it can be argued that canonical structures seem to have a rather natural place in ED; arising from conservation laws in [3]}[4]} and alternatively from symmetry considerations [5]}. However, from another perspective entirely, the use of a canonical formalism in ED can also be traced to more pragmatic concerns, as it allows one to borrow from a roster of covariant canonical techniques designed in the context of classical physics (see e.g., [6]}), but deployed for the purposes of ED. These together suggest that we view the canonical setting, and the symplectic symmetries that undergird it, as a central criterion for updating in ED.
